Nuprl Lemma : req_int_terms_weakening
∀[t1,t2:int_term()]. t1 ≡ t2 supposing t1 = t2 ∈ int_term()
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
int_term: int_term(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
req_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
real_wf,
req_witness,
real_term_value_wf,
equal_wf,
int_term_wf,
req_weakening,
req_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
functionEquality,
intEquality,
extract_by_obid,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
functionExtensionality,
applyEquality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_isectElimination,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination
Latex:
\mforall{}[t1,t2:int\_term()]. t1 \mequiv{} t2 supposing t1 = t2
Date html generated:
2017_10_02-PM-07_18_30
Last ObjectModification:
2017_04_02-PM-11_43_57
Theory : reals
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