Nuprl Lemma : proj-eq_transitivity
∀[n:ℕ]. ∀[a,b,c:ℙ^n]. (a = c) supposing (b = c and a = b)
Proof
Definitions occuring in Statement :
proj-eq: a = b,
real-proj: ℙ^n,
nat: ℕ,
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_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
proj-eq: a = b,
all: ∀x:A. B[x],
real-proj: ℙ^n,
real-vec: ℝ^n,
implies: P ⇒ Q,
nat: ℕ,
prop: ℙ,
guard: {T},
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
proj-eq-equiv,
req_witness,
rmul_wf,
int_seg_wf,
proj-eq_wf,
real-proj_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
applyEquality,
setElimination,
rename,
hypothesis,
because_Cache,
independent_functionElimination,
natural_numberEquality,
addEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b,c:\mBbbP{}\^{}n]. (a = c) supposing (b = c and a = b)
Date html generated:
2017_10_05-AM-00_18_35
Last ObjectModification:
2017_06_17-AM-10_07_50
Theory : inner!product!spaces
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