Nuprl Lemma : proj-eq_functionality
∀[n:ℕ]. ∀[x1,x2,y1,y2:ℙ^n]. (uiff(x1 = y1;x2 = y2)) supposing (y1 = y2 and x1 = x2)
Proof
Definitions occuring in Statement :
proj-eq: a = b,
real-proj: ℙ^n,
nat: ℕ,
uiff: uiff(P;Q),
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,
uiff: uiff(P;Q),
and: P ∧ Q,
guard: {T},
proj-eq: a = b,
all: ∀x:A. B[x],
real-proj: ℙ^n,
real-vec: ℝ^n,
implies: P ⇒ Q,
nat: ℕ,
prop: ℙ
Lemmas referenced :
proj-eq_inversion,
proj-eq_transitivity,
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,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
applyEquality,
setElimination,
rename,
because_Cache,
independent_functionElimination,
natural_numberEquality,
addEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x1,x2,y1,y2:\mBbbP{}\^{}n]. (uiff(x1 = y1;x2 = y2)) supposing (y1 = y2 and x1 = x2)
Date html generated:
2017_10_05-AM-00_18_43
Last ObjectModification:
2017_06_17-AM-10_08_15
Theory : inner!product!spaces
Home
Index