Nuprl Lemma : trivial-subterm
∀[opr:Type]. ∀f:opr. ∀bts:bound-term(opr) List. ∀i:ℕ||bts||. snd(bts[i]) << mkterm(f;bts)
Proof
Definitions occuring in Statement :
subterm: s << t,
bound-term: bound-term(opr),
mkterm: mkterm(opr;bts),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
pi2: snd(t),
all: ∀x:A. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
bound-term: bound-term(opr),
pi2: snd(t),
immediate-subterm: s < t,
cand: A c∧ B
Lemmas referenced :
immediate-is-subterm,
select_wf,
bound-term_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
length_wf,
intformless_wf,
int_formula_prop_less_lemma,
mkterm_wf,
term_wf,
int_seg_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
setElimination,
rename,
because_Cache,
independent_isectElimination,
productElimination,
imageElimination,
natural_numberEquality,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
sqequalRule,
independent_pairFormation,
universeIsType,
voidElimination,
inhabitedIsType,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
productIsType,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}f:opr. \mforall{}bts:bound-term(opr) List. \mforall{}i:\mBbbN{}||bts||. snd(bts[i]) << mkterm(f;bts)
Date html generated:
2020_05_19-PM-09_54_17
Last ObjectModification:
2020_03_10-PM-01_46_13
Theory : terms
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