Nuprl Lemma : immediate-subterm_wf
∀[opr:Type]. ∀[s,t:term(opr)]. (s < t ∈ ℙ)
Proof
Definitions occuring in Statement :
immediate-subterm: s < t,
term: term(opr),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
immediate-subterm: s < t,
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
bound-term: bound-term(opr),
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
pi2: snd(t)
Lemmas referenced :
list_wf,
bound-term_wf,
equal_wf,
term_wf,
mkterm_wf,
int_seg_wf,
length_wf,
select_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,
intformless_wf,
int_formula_prop_less_lemma,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
natural_numberEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
productElimination,
imageElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
inhabitedIsType,
lambdaFormation_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[s,t:term(opr)]. (s < t \mmember{} \mBbbP{})
Date html generated:
2020_05_19-PM-09_54_04
Last ObjectModification:
2020_03_09-PM-04_08_30
Theory : terms
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