Nuprl Lemma : ringeq_int_terms_transitivity
∀[r:Rng]. ∀[t1,t2,t3:int_term()]. (t1 ≡ t3) supposing (t2 ≡ t3 and t1 ≡ t2)
Proof
Definitions occuring in Statement :
ringeq_int_terms: t1 ≡ t2,
rng: Rng,
int_term: int_term(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
rng: Rng,
prop: ℙ,
squash: ↓T,
all: ∀x:A. B[x],
ringeq_int_terms: t1 ≡ t2,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
int_term_wf,
ringeq_int_terms_wf,
iff_weakening_equal,
ring_term_value_wf,
rng_car_wf,
true_wf,
squash_wf,
equal_wf
Rules used in proof :
isect_memberEquality,
intEquality,
functionEquality,
axiomEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
natural_numberEquality,
because_Cache,
functionExtensionality,
dependent_functionElimination,
rename,
setElimination,
universeEquality,
equalitySymmetry,
hypothesis,
equalityTransitivity,
hypothesisEquality,
isectElimination,
extract_by_obid,
imageElimination,
lambdaEquality,
thin,
applyEquality,
lambdaFormation,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[t1,t2,t3:int\_term()]. (t1 \mequiv{} t3) supposing (t2 \mequiv{} t3 and t1 \mequiv{} t2)
Date html generated:
2018_05_21-PM-03_16_01
Last ObjectModification:
2018_01_25-PM-02_18_31
Theory : rings_1
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