Nuprl Lemma : mFOL-sequent-evidence-trivial
Uniform evidence for a trivially true sequent where the conclusion is
a given member of the hypotheses.⋅
∀hyps:mFOL() List. ∀i:ℕ||hyps||.  mFOL-sequent-evidence(<hyps, hyps[i]>)
Proof
Definitions occuring in Statement : 
mFOL-sequent-evidence: mFOL-sequent-evidence(s)
, 
mFOL: mFOL()
, 
select: L[n]
, 
length: ||as||
, 
list: T List
, 
int_seg: {i..j-}
, 
all: ∀x:A. B[x]
, 
pair: <a, b>
, 
natural_number: $n
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
mFOL-sequent-evidence: mFOL-sequent-evidence(s)
, 
mFO-uniform-evidence: mFO-uniform-evidence(vs;fmla)
, 
mFOL-sequent-abstract: mFOL-sequent-abstract(s)
, 
FOSatWith: Dom,S,a |= fmla
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
int_seg: {i..j-}
, 
guard: {T}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
top: Top
, 
prop: ℙ
, 
less_than: a < b
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
cand: A c∧ B
, 
mFOL-hyps-meaning: mFOL-hyps-meaning(Dom;S;a;hyps)
, 
le: A ≤ B
, 
mFOL-sequent: mFOL-sequent()
Lemmas referenced : 
mFOL-abstract_wf, 
mFOL-sequent-freevars-subset-1, 
subtype_rel_FOAssignment, 
mFOL-freevars_wf, 
FOSatWith_wf, 
lelt_wf, 
top_wf, 
subtype_rel_list, 
select-map, 
length-map, 
le_wf, 
select-tuple_wf, 
list_wf, 
int_seg_wf, 
FOStruct_wf, 
int_formula_prop_less_lemma, 
intformless_wf, 
decidable__lt, 
int_formula_prop_wf, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
length_wf, 
int_seg_properties, 
mFOL_wf, 
mFOL-sequent-freevars_wf, 
FOAssignment_wf, 
select_wf, 
mFOL-hyps-meaning_wf, 
tuple-type_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
isect_memberFormation, 
sqequalRule, 
introduction, 
lambdaEquality, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
independent_isectElimination, 
hypothesis, 
hypothesisEquality, 
independent_pairEquality, 
setElimination, 
rename, 
natural_numberEquality, 
productElimination, 
dependent_functionElimination, 
unionElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
computeAll, 
imageElimination, 
applyEquality, 
cumulativity, 
universeEquality, 
dependent_set_memberEquality, 
productEquality
Latex:
\mforall{}hyps:mFOL()  List.  \mforall{}i:\mBbbN{}||hyps||.    mFOL-sequent-evidence(<hyps,  hyps[i]>)
Date html generated:
2016_07_08-PM-05_21_10
Last ObjectModification:
2016_01_16-PM-04_32_26
Theory : minimal-first-order-logic
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