Nuprl Lemma : equiv_int_terms_transitivity
∀[t1,t2,t3:int_term()]. (t1 ≡ t3) supposing (t2 ≡ t3 and t1 ≡ t2)
Proof
Definitions occuring in Statement :
equiv_int_terms: t1 ≡ t2,
int_term: int_term(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
equiv_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
int_term_value_wf,
iff_weakening_equal,
equiv_int_terms_wf,
int_term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
applyEquality,
thin,
lambdaEquality,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
intEquality,
dependent_functionElimination,
functionExtensionality,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
functionEquality,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[t1,t2,t3:int\_term()]. (t1 \mequiv{} t3) supposing (t2 \mequiv{} t3 and t1 \mequiv{} t2)
Date html generated:
2017_04_14-AM-08_57_29
Last ObjectModification:
2017_02_27-PM-03_40_46
Theory : omega
Home
Index